This proposal addresses statistical issues arising from measurement error problems, with an emphasis on modeling within a Bayesian framework. Measurement error arises when a variable of interest, such as exposure to a contaminant, cannot be measured or is too expensive to measure for most subjects. Instead inference must based on a proxy variable measured with error, which can lead to incorrect conclusions if not properly addressed. This proposal is motivated by applications in environmental health studies, in which measurement error is often a problem. The specific aims are: (1) To delineate the advantages and disadvantages of Bayesian and frequentist approaches to measurement error problems using a case study approach; (2) Within a Bayesian framework, to examine the sensitivity of numerical estimates of the relationship between the outcome and covariates to their assumed distributions; (3) To develop a Bayesian paradigm for the 2-stage case- control design, and to compare numerical estimates with those from frequentist methods; and (4) To develop efficient sampling strategies for measuring the "gold standard" in a validation sub-study within a repeated measures setting. The research will be illustrated and applied to several datasets collected for environmental health studies.